Annotated Answer Key
Name______________________
Grade 5, Unit 1, Lesson 8: Decompose and recompose solid figures by partitioning
figures into layers
Use unit cubes to build models to help you answer the questions below.
1. Decompose the figure below to
determine how many unit cubes make up
the base. How many unit cubes make up
the base of the figure?
2. Decompose the figure below to
determine how many unit cubes make up
the base. How many unit cubes make up
the base of the figure?
12 unit cubes
NOTE: ​
Remind students that the base of
a rectangular prism can refer to the top
or bottom layer. Either way the answer
will still be 12 unit cubes because all
layers in a rectangular prism have an
equal number of unit cubes.
3. Decompose the figure below to
determine how many unit cubes make up
each horizontal layer. How many unit
cubes make up each horizontal layer of
the figure?
6 unit cubes
4. One horizontal layer of a rectangular
prism is shown below. A total of 4 layers
make up the original figure. Recompose
the figure to determine the volume of the
original rectangular prism. What is the
volume of the recomposed rectangular
prism?
© LearnZillion, Inc. 2015. All Rights Reserved. No part of this document may be
reproduced without LearnZillion's express consent.
Annotated Answer Key
Name______________________
Grade 5, Unit 1, Lesson 8: Decompose and recompose solid figures by partitioning
figures into layers
60 cubic units or 50 unit cubes or 50
units cubed
24 unit cubes
NOTE:​
Make sure to have students use
unit cube manipulatives when solving
these problems. They should be able to
show you how to build the model,
decompose it into horizontal layers, and
easily see that each layer is made up of
the same number of unit cubes.
5. Decompose the figure below to
determine how many unit cubes make up
each vertical layer. How many unit cubes
make up each vertical layer of the figure?
NOTE:​
Make sure students include the
units in their answer.
6. One vertical layer of a rectangular
prism is shown below. A total of 3
vertical layers make up the original figure.
Recompose the figure to determine the
volume of the original rectangular prism.
What is the volume of the recomposed
rectangular prism?
© LearnZillion, Inc. 2015. All Rights Reserved. No part of this document may be
reproduced without LearnZillion's express consent.
Annotated Answer Key
Name______________________
Grade 5, Unit 1, Lesson 8: Decompose and recompose solid figures by partitioning
figures into layers
8 unit cubes
30 cubic units or 30 units cubed or 30
unit cubes
7. Decompose the irregular figure shown
below to determine its volume. What is
the volume of the figure?
12 unit cubes or 12 cubic units or 12
units cubed
8. Decompose the irregular figure shown
below to determine its volume. What is
the volume of the figure?
14 unit cubes or 14 cubic units or 14
units cubed
NOTE:​
Encourage students to build the
irregular figure with unit cube
manipulatives and explain how and why
they decided to decompose the figure in
© LearnZillion, Inc. 2015. All Rights Reserved. No part of this document may be
reproduced without LearnZillion's express consent.
Annotated Answer Key
Name______________________
Grade 5, Unit 1, Lesson 8: Decompose and recompose solid figures by partitioning
figures into layers
a particular way.
9. Leila is cleaning up dice for her
teacher by putting them away in a plastic
bin as shown below. The image below
shows how many dice Leila has already
put away in the bing. What is the most
amount of dice that can fit in the bin?
10. Michael is helping his school’s
librarian stack boxes of books. Each box
has a volume of one unit cube. So far
he’s stacked one layer of boxes as
shown below. If Michael stacks two more
layers, what will the volume of the entire
stack of boxes be?
48 unit cubes or 48 cubic units or 48
units cubed
24 dice will fit in the plastic bin
© LearnZillion, Inc. 2015. All Rights Reserved. No part of this document may be
reproduced without LearnZillion's express consent.